* To stop sleeping with Claudius: Hamlet is disgusted by his mother's hasty marriage to his uncle, Claudius, and believes it is incestuous. He begs her to repent her actions and stop sleeping with Claudius.
* To "remember" his father: Hamlet urges his mother to remember her deceased husband, King Hamlet, and the love they shared. He wants her to acknowledge the wrong she has done by marrying Claudius so quickly after his father's death.
* To refrain from criticizing him: Hamlet is aware that he is acting strangely and emotionally, but he wants his mother to understand his reasons and not criticize him. He asks her to forgive him for his actions and to simply listen to him.
* To be honest with Claudius: Hamlet encourages his mother to be honest with Claudius about his guilt and his "wicked deeds" and to tell him that she regrets marrying him.
It's important to note that while Hamlet expresses his desire for his mother to change her behavior, he doesn't actually demand it. Instead, he appeals to her love and conscience, hoping she will see the error of her ways and choose a different path.